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   "source": [
    "# 第二次作业第6题\n",
    "作者：赵飞\n",
    "学号：202018019427078\n",
    "日期：2021-04-26"
   ],
   "cell_type": "markdown",
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  },
  {
   "cell_type": "code",
   "execution_count": 22,
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   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def df(y, t, M, k, b, F):\n",
    "    '''\n",
    "    弹簧系统所满足微分方程 (x1=dx/dt)\n",
    "    '''\n",
    "    x, x1 = y\n",
    "    return [x1, (F-k*x-b*x1)/M]\n",
    "# 参数及初值\n",
    "M, k, b, F = 1.0, 0.5, 0.2, 1.0\n",
    "y0 = [-1, 0.0]\n",
    "# 求解\n",
    "t = np.arange(0, 50, 0.02)  # 观测时间\n",
    "y = integrate.odeint(df, y0, t, args=(M,k,b,F))\n",
    "plt.plot(t, y[:, 0], label='x (position of Spring)')\n",
    "plt.plot(t, y[:, 1], label='dx/dt (speed of Spring)')\n",
    "# 展示弹簧位置、速度随时间变化\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ]
}